Question

The following function defines a recursive sequence:

f(0) = -4

f(1) = 12

f(n) = -3•f(n -1) - 2•f(n - 2); for n > 1

Which of the following sequences is defined by this recursive function?

A. -4, 12, -28, 60, …

B. -4, -12, -28, -60, …

C. -4, 12, -18, 54, …

D. -4, 12, -18, -54, …
I don't understand this question at all, Can anyone help me?

Answer 1

\[f(n)=-3\cdot f(n-1)-2\cdot f(n-2)\]let's use n=2\[f(2)=-3\cdot f(2-1)-2\cdot f(2-2)\]\[f(2)=-3\cdot f(1)-2\cdot f(0)\]now we replace the value that we have\[f(1)=12~~and~~f(0)=-4\]\[f(2)=-3\cdot12-2\cdot(-4)\]\[f(2)=-36+8\]\[\boxed{\boxed{f(2)=-28}}\]now we ahve to find the other term, when n=3\[f(n)=-3\cdot f(n-1)-2\cdot f(n-2)\]\[f(3)=-3\cdot f(3-1)-2\cdot f(3-2)\]\[f(3)=-3\cdot f(2)-2\cdot f(1)\]\[f(3)=-3\cdot(-28)-2\cdot12\]\[f(3)=84-24\]\[\boxed{\boxed{f(3)=60}}\]Therefore we got the sequence\[\{-4,12,-28,60,...\}\]

Answer 2

wow thank you

Answer 3

You're welcome